Aimed at the problems, of analysis on band gap of electromagnetic crystal using usual method, such as time-consuming, hard to be understood, a model of plane wave expansion （PWE） method is introduced in this paper and the plane wave expansion method is adopted to analyze the band gap structure of two-dimensional electromagnetic crystal with different shape of filling cell. By using this method, electrical field or magnetic field and dielectric constant or its reciprocal are expanded in the form of double Fourier series, which are then substituted into the scalar wave equation they must fulfill. Again, a characteristic equation for 2-D electromagnetic crystal is achieved, and by solving it the band gap structure is obtained. Moreover, two equivalent structures are introduced. The results of calculation show that the size of filling cell and the relative dielectric constant all have influence on band gap structure. Comparison between the numerical solution and literature data indicates that the method in this paper is valid. At last, two equivalent structures are obtained by using periodic prolongation. It is not required to deduce the structure coefficients, and the analysis of band gap structure using the model of plane wave expansion method is realized, so simplification of analysis is achieved.